Problem: Simplify the following expression: $q = \dfrac{y^2 + 15y + 54}{y + 6} $
Explanation: First factor the polynomial in the numerator. $ y^2 + 15y + 54 = (y + 6)(y + 9) $ So we can rewrite the expression as: $q = \dfrac{(y + 6)(y + 9)}{y + 6} $ We can divide the numerator and denominator by $(y + 6)$ on condition that $y \neq -6$ Therefore $q = y + 9; y \neq -6$